When using a walking foot for making wavy lines, it's a matter of gently moving the quilt sandwich as it feeds into the walking foot. I never had difficulty with it, so I'm not sure I understand the problem.
Regarding FMQ, have you tried doing it with the feed dogs up? That can help with the jumping around problem.
Otherwise, I do not see that sewing horizontally would be any easier than sewing the length of the quilt. It could be more difficult because there would be more bulk under the arm of the machine to manage.